George Green (mathematician)

George Green (14 July 1793 – 31 May 1841) was a British mathematical physicist born in Sneinton, Nottinghamshire, now part of the city of Nottingham. Despite receiving little recognition during his lifetime, he is best remembered for his Essay on electricity and magnetism published in 1828. In this essay he introduced an early version of Green's theorem in vector calculus, the notion of potential functions as currently used in physics, and a method of solving differential equations called Green's functions. This paper formed the foundation for the work of later scientists such as William Thomson (later Lord Kelvin), among many others. His work on potentials ran parallel to that of Carl Friedrich Gauss. As a mathematician, he was almost entirely self-taught, receiving only about one year of formal schooling as a child, between the ages of eight and nine. Green then worked his father's bakery from a young age, and later at the mill his father constructed in 1807, now known as Green's Windmill. Whilst working as a miller, he became a member of Nottingham Subscription Library through which he was able to access contemporary mathematical knowledge. Green formed a relationship with Jane Smith, the daughter of the mill manager William Smith. Although the couple never married, they had seven children together and she later adopted Green's surname. After the death of his father in 1829, he was left a substantial inheritance, allowing him to give up milling to pursue mathematics. In 1833, Green began a formal education at the University of Cambridge and was elected a fellow at Caius College after his graduation. Throughout his time at the university, he wrote six papers on hydrodynamics, acoustics, and optics. In 1840, he fell ill and returned to Nottingham where he died of influenza the following year, on 31 May 1841. After his death, his Essay was rediscovered by William Thomson (later Lord Kelvin) who promoted Green's work and used it in his own research on electricity and magnetism. Today, Green's functions remain a standard tool for solving differential equations in modern physics, including in quantum electrodynamics (QED) and condensed-matter physics.

Early life Green was born and lived for most of his life in the English town of Sneinton, Nottinghamshire, now part of the city of Nottingham which then had a population of around 30,000. He was baptized on 14 July 1793. His father, also named George, was a baker who had built and owned a brick windmill used to grind grain.

Robert Goodacre's Academy During this era, most children received little schooling beyond being taught to read and write at Sunday schools. Green was fortunate in that his father was able and willing to have him privately educated. He entered the academy of Robert Goodacre, a man known for his enthusiasm towards the sciences and education. The academy's "philosophical instruments" included an "electrical machine" and an orrery. However, Green stayed for only 18 months before returning to work at his father's bakery.

Move from Nottingham to Sneinton In 1773 George's father moved to Nottingham, which at the time had a reputation for being a pleasant town with open spaces and wide roads. By 1831, however, the population had increased nearly five times, in part due to the budding Industrial Revolution, and the city became known as one of the worst slums in England. There were frequent riots by starving workers, often associated with special hostility towards bakers and millers on the suspicion that they were hiding grain to drive up food prices. For these reasons, in 1807, George Green senior bought a plot of land in Sneinton. On this plot of land he built a "brick wind corn mill", now referred to as Green's Windmill. It was technologically impressive for its time, but required nearly twenty-four-hour maintenance, which was to become Green's burden for the next twenty years.

Adult life

Miller

Just as with baking, Green found the responsibilities of operating the mill annoying and tedious. Grain from the fields was arriving continuously at the mill's doorstep, and the sails of the windmill had to be constantly adjusted to the wind speed, both to prevent damage in high winds, and to maximise rotational speed in low winds. The millstones that would continuously grind against each other, could wear down or cause a fire if they ran out of grain to grind. Every month the stones, which weighed over a ton, would have to be replaced or repaired.

Family life In 1823 Green formed a relationship with Jane Smith, the daughter of William Smith, hired by Green Senior as mill manager. Although Green and Jane Smith never married, Jane eventually became known as Jane Green and the couple had seven children together; all but the first had Green as a baptismal name. The youngest child was born 13 months before Green's death. Green provided for his (so-called) common-law wife and children in his will.

Nottingham Subscription Library When Green was thirty, he became a member of the Nottingham Subscription Library, then the intellectual heart of the town. It still exists today as the Bromley House Library. This library was likely the main source of Green's advanced mathematical knowledge, giving him access to the Philosophical Transactions of the Royal Society, among other scientific journals. While foreign journals were not available, the Transactions did mention their contents, which allowed Green to obtain reprints directly from their authors.

Formal education and academic career

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